A classmate cut a part of a flat ginkgo leaf along a straight line with scissors and found that the circumference of the remaining ginkgo leaf was smaller than the original ginkgo leaf. What mathematical knowledge can correctly explain this phenomenon?

Solution: Because the axiom of line segment: between two points, the line segment is the shortest, so the perimeter of the remaining leaves is smaller than that of the original leaves. This question mainly examines the properties of line segments, and the key to solving the problem is to master the theorem about line segments; Cutting off a part is equivalent to replacing the original curve connected by two points with a segment. Do you have any ideas? This phenomenon can be explained by recalling the axioms of line segments.

Mathematics [English: Mathematics, from ancient Greece μ? θξμα(máthēma)； Often abbreviated as math or maths], it is a discipline that studies concepts such as quantity, structure, change, space and information.

Mathematics is a universal means for human beings to strictly describe and deduce the abstract structure and mode of things, and can be applied to any problem in the real world. All mathematical objects are artificially defined in essence.

In this sense, mathematics belongs to formal science, not natural science. Different mathematicians and philosophers have a series of views on the exact scope and definition of mathematics.

Mathematics plays an irreplaceable role in the development of human history and social life, and it is also an indispensable basic tool for studying and studying modern science and technology.

Aristotle defined mathematics as "quantitative mathematics", which lasted until18th century.

/kloc-since the 0/9th century, mathematical research has become more and more rigorous, and it has begun to involve abstract topics such as group theory and projection geometry that have no clear relationship with quantity and measurement. Mathematicians and philosophers have begun to put forward various new definitions. Some of these definitions emphasize the deductive nature of a lot of mathematics, some emphasize its abstraction, and some emphasize some themes in mathematics.

Even among professionals, the definition of mathematics has not been reached. Whether mathematics is an art or a science has not even been decided. Many professional mathematicians are not interested in the definition of mathematics or think it is undefined.

Some just said, "Mathematics is done by mathematicians." The three main mathematical definitions are called logicians, intuitionists and formalists, each of which reflects a different school of philosophical thought. Everyone has serious problems, no one generally accepts it, and no reconciliation seems feasible.

The early definition of mathematical logic is Benjamin Peirce's "science that draws inevitable conclusions".

In Principles of Mathematics, Bertrand Russell and alfred north whitehead put forward a philosophical program called logicism, trying to prove that all mathematical concepts, statements and principles can be defined and proved by symbolic logic. The logical definition of mathematics is Russell's "All mathematics is symbolic logic" (1903).

The definition of intuitionism comes from mathematician L.E.J.Brouwer, who equates mathematics with some psychological phenomena. An example of the definition of intuitionism is that mathematics is a psychological activity constructed one after another.

Intuitionism is characterized by rejecting some mathematical ideas that are considered effective according to other definitions. In particular, although other mathematical philosophies allow objects that can be proved to exist, even if they cannot be constructed, intuitionism only allows mathematical objects that can actually be constructed.